The differential branching fraction of the rare decay $\Lambda^{0}_{b}
\rightarrow \Lambda \mu^+\mu^-$ is measured as a function of $q^{2}$, the
square of the dimuon invariant mass. The analysis is performed using
proton-proton collision data, corresponding to an integrated luminosity of $3.0
\mbox{ fb}^{-1}$, collected by the LHCb experiment. Evidence of signal is
observed in the $q^2$ region below the square of the $J/\psi$ mass. Integrating
over $15 < q^{2} < 20 \mbox{ GeV}^2/c^4$ the branching fraction is measured as
$d\mathcal{B}(\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^-)/dq^2 = (1.18 ^{+
0.09} _{-0.08} \pm 0.03 \pm 0.27) \times 10^{-7} ( \mbox{GeV}^{2}/c^{4})^{-1}$,
where the uncertainties are statistical, systematic and due to the
normalisation mode, $\Lambda^{0}_{b} \rightarrow J/\psi \Lambda$, respectively.
In the $q^2$ intervals where the signal is observed, angular distributions are
studied and the forward-backward asymmetries in the dimuon ($A^{l}_{\rm FB}$)
and hadron ($A^{h}_{\rm FB}$) systems are measured for the first time. In the
range $15 < q^2 < 20 \mbox{ GeV}^2/c^4$ they are found to be $A^{l}_{\rm FB} =
-0.05 \pm 0.09 \mbox{ (stat)} \pm 0.03 \mbox{ (syst)}$ and $A^{h}_{\rm FB} =
-0.29 \pm 0.07 \mbox{ (stat)} \pm 0.03 \mbox{ (syst)}$.

A search is presented for massive long-lived particles decaying into a muon
and two quarks. The dataset consists of proton-proton interactions at
centre-of-mass energies of 7 and 8 TeV, corresponding to integrated
luminosities of 1 and 2 1/fb, respectively. The analysis is performed assuming
a set of production mechanisms with simple topologies, including the production
of a Higgs-like particle decaying into two long-lived particles. The mass range
from 20 to 80 GeV and lifetimes from 5 to 100 ps are explored. Results are also
interpreted in terms of neutralino production in different supersymmetric
models, with masses in the 23-198 GeV range. No excess above the background
expectation is observed and upper limits are set on the production
cross-section for various points in the parameter space of theoretical models.

The $\Lambda_b^0\to\Lambda\phi$ decay is observed using data corresponding to
an integrated luminosity of 3.0fb$^{-1}$ recorded by the LHCb experiment. The
decay proceeds at leading order via a $b\to s\bar{s}s$ loop transition and is
therefore sensitive to the possible presence of particles beyond the Standard
Model. A first observation is reported with a significance of $5.9$ standard
deviations. The value of the branching fraction is measured to be
$(5.18\pm1.04\pm0.35\,^{+0.67}_{-0.62})\times10^{-6}$, where the first
uncertainty is statistical, the second is systematic, and the third is related
to external inputs. Triple-product asymmetries are measured to be consistent
with zero.

A search for $C$P and $P$ violation using triple-product asymmetries is
performed with $\Lambda^{0}_{b}\to pK^{-}\pi^{+}\pi^{-}$, $\Lambda^{0}_{b}\to
pK^{-}K^{+}K^{-}$ and $\Xi^{0}_{b}\to pK^{-}K^{-}\pi^{+}$ decays. The data
sample corresponds to integrated luminosities of 1.0fb$^{-1}$ and 2.0fb$^{-1}$,
recorded with the LHCb detector at centre-of-mass energies of 7TeV and 8TeV,
respectively. The $CP$- and $P$-violating asymmetries are measured both
integrating over all phase space and in specific phase-space regions. No
significant deviation from $CP$ or $P$ symmetry is found.

A measurement of the $CP$ asymmetries $S_{f}$ and $S_{\bar{f}}$ in $B^0\to
D^{\mp}\pi^{\pm}$ decays is reported. The decays are reconstructed in a dataset
collected with the LHCb experiment in proton-proton collisions at
centre-of-mass energies of 7 and 8 TeV and corresponding to an integrated
luminosity of $3.0 \rm{ fb}^{-1}$. The $CP$ asymmetries are measured to be
$S_{f} = 0.058 \pm 0.020 (\rm{stat}) \pm 0.011(\rm{syst})$ and $S_{\bar{f}} =
0.038\pm 0.020 (\text{stat})\pm 0.007 (\text{syst})$. These results are in
agreement with, and more precise than, previous determinations. They are used
to constrain $|\sin\left(2\beta+\gamma\right)|$ and $\gamma$ to intervals that
are consistent with the current world-average values.

The ratio of branching fractions ${\cal{R}}(D^{*-})\equiv {\cal{B}}(B^0 \to
D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$ is measured
using a data sample of proton-proton collisions collected with the LHCb
detector at center-of-mass energies of 7 and 8 TeV, corresponding to an
integrated luminosity of 3$~$fb$^{-1}$. The $\tau$ lepton is reconstructed with
three charged pions in the final state. A novel method is used that exploits
the different vertex topologies of signal and backgrounds to isolate samples of
semitauonic decays of $b$ hadrons with high purity. Using the $B^0 \to
D^{*-}\pi^+\pi^-\pi^+$ decay as the normalization channel, the ratio
${\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to
D^{*-}\pi^+\pi^-\pi^+)$ is measured to be $1.97 \pm 0.13 \pm 0.18$, where the
first uncertainty is statistical and the second systematic. An average of
branching fraction measurements for the normalization channel is used to derive
${\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau}) = (1.42 \pm 0.094 \pm 0.129 \pm
0.054) \%$, where the third uncertainty is due to the limited knowledge of
${\cal{B}}(B^0\to D^{*-}\pi^+\pi^-\pi^+)$. A test of lepton flavor universality
is performed using the well-measured branching fraction ${\cal{B}}(B^0 \to
D^{*-} \mu^+\nu_{\mu})$ to compute ${\cal{R}}(D^{*-}) = 0.291 \pm 0.019 \pm
0.026 \pm 0.013$, where the third uncertainty originates from the uncertainties
on ${\cal{B}}(B^0 \to D^{*-}\pi^+\pi^-\pi^+)$ and ${\cal{B}}(B^0 \to D^{*-}
\mu^+\nu_{\mu})$. This measurement is in agreement with the Standard Model
prediction and with previous measurements.

The ratio of branching fractions ${\cal{R}}(D^{*-})\equiv {\cal{B}}(B^0 \to
D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$ is measured
using a data sample of proton-proton collisions collected with the LHCb
detector at center-of-mass energies of 7 and 8 Tev, corresponding to an
integrated luminosity of 3$~$fb$^{-1}$. For the first time ${\cal{R}}(D^{*-})$
is determined using the $\tau$ lepton decays with three charged pions in the
final state. The $B^0 \to D^{*-} \tau^+\nu_{\tau}$ yield is normalized to that
of the $B^0\to D^{*-} \pi^+\pi^-\pi^+$ mode, providing a measurement of
${\cal{B}}(B^0\to D^{*-}\tau^+\nu_{\tau})/{\cal{B}}(B^0\to
D^{*-}\pi^+\pi^-\pi^+) = 1.97 \pm 0.13 \pm 0.18$, where the first uncertainty
is statistical and the second systematic. The value of ${\cal{B}}(B^0 \to
D^{*-} \tau^+ \nu_{\tau}) = (1.42 \pm 0.094 \pm 0.129 \pm 0.054)\% $ is
obtained, where the third uncertainty is due to the limited knowledge of the
branching fraction of the normalization mode. Using the well-measured branching
fraction of the $B^0 \to D^{*-} \mu^+\nu_{\mu}$ decay, a value of
${\cal{R}}(D^{*-}) = 0.291 \pm 0.019 \pm 0.026 \pm 0.013$ is established, where
the third uncertainty is due to the limited knowledge of the branching
fractions of the normalization and $B^0\to D^{*-}\mu^+\nu_{\mu}$ modes. This
measurement is in agreement with the Standard Model prediction and with
previous results.

The production cross-sections of $\Upsilon(1S)$, $\Upsilon(2S)$ and
$\Upsilon(3S)$ mesons in proton-proton collisions at $\sqrt{s}$= 13 TeV are
measured with a data sample corresponding to an integrated luminosity of $277
\pm 11$ $\rm pb^{-1}$ recorded by the LHCb experiment in 2015. The $\Upsilon$
mesons are reconstructed in the decay mode $\Upsilon\to\mu^{+}\mu^{-}$. The
differential production cross-sections times the dimuon branching fractions are
measured as a function of the $\Upsilon$ transverse momentum, $p_{\rm T}$, and
rapidity, $y$, over the range $0 < p_{\rm T}< 30$ GeV/c and $2.0 < y < 4.5$.
The ratios of the cross-sections with respect to the LHCb measurement at
$\sqrt{s}$= 8 TeV are also determined. The measurements are compared with
theoretical predictions based on NRQCD.

The difference between the $CP$ asymmetries in the decays $\varLambda_{c}^{+}
\to pK^{-}K^{+}$ and $\varLambda_{c}^{+} \to p\pi^{-}\pi^{+}$ is presented.
Proton-proton collision data taken at centre-of-mass energies of $7$ and
$8\,\mathrm{TeV}$ collected by the LHCb detector in 2011 and 2012 are used,
corresponding to an integrated luminosity of $3\,\mathrm{fb}^{-1}$. The
$\varLambda_{c}^{+}$ candidates are reconstructed as part of the
$\varLambda_{b}^{0} \to \varLambda_{c}^{+}\mu^{-}X$ decay chain. In order to
maximize the cancellation of production and detection asymmetries in the
difference, the final-state kinematic distributions of the two samples are
aligned by applying phase-space-dependent weights to the $\varLambda_{c}^{+}
\to p\pi^{-}\pi^{+}$ sample. This alters the definition of the integrated $CP$
asymmetry to $A_{CP}^{\text{wgt}}(p\pi^{-}\pi^{+})$. Both samples are corrected
for reconstruction and selection efficiencies across the five-dimensional
$\varLambda_{c}^{+}$ decay phase space. The difference in $CP$ asymmetries is
found to be \begin{align*}
\Delta{A^{\text{wgt}}_{CP}} &= A_{CP}(pK^{-}K^{+}) -
A_{CP}^{\text{wgt}}(p\pi^{-}\pi^{+})\\
&= (0.30 \pm 0.91 \pm 0.61)\,\%, \end{align*} where the first uncertainty is
statistical and the second is systematic.

A search for the decay $B_{s}^0 \rightarrow \overline{K}{}^{*0}\mu^+\mu^-$ is
presented using data sets corresponding to 1.0, 2.0 and 1.6 $\text{fb}^{-1}$ of
integrated luminosity collected during $pp$ collisions with the LHCb experiment
at centre-of-mass energies of 7, 8 and 13 TeV, respectively. An excess is found
over the background-only hypothesis with a significance of 3.4 standard
deviations. The branching fraction of the $B_{s}^0 \rightarrow
\overline{K}{}^{*0}\mu^+\mu^-$ decay is determined to be $\mathcal{B}(B_{s}^0
\rightarrow \overline{K}{}^{*0}\mu^+\mu^-) = [2.9 \pm 1.0~(\text{stat}) \pm
0.2~(\text{syst}) \pm 0.3~(\text{norm})] \times 10^{-8}$, where the first and
second uncertainties are statistical and systematic, respectively. The third
uncertainty is due to limited knowledge of external parameters used to
normalise the branching fraction measurement.

Measurements of the cross-section for producing \bquark quarks in the
reaction $pp\to b\bar{b} X$ are reported in 7 and 13 TeV collisions at the LHC
as a function of the pseudorapidity $\eta$ in the range $2<\eta<5$ covered by
the acceptance of the LHCb experiment. The measurements are done using
semileptonic decays of $b$-flavored hadrons decaying into a ground-state
charmed hadron in association with a muon. The cross-sections in the covered
$\eta$ range are $72.0\pm 0.3\pm6.8~\mu$b and $144\pm 1\pm 21~\mu$b for 7 and
13 TeV. The ratio is $2.00\pm0.02\pm0.26$, where the quoted uncertainties are
statistical and systematic, respectively. The agreement with theoretical
expectation is good at 7 TeV, but differs somewhat at 13 TeV. The measured
ratio of cross-sections is larger at lower $\eta$ than the model prediction.

A search for $C\!P$ violation in the decay $\Lambda^0_b \to p K^- \mu^+
\mu^-$ is presented. This decay is mediated by flavour-changing neutral-current
transitions in the Standard Model and is potentially sensitive to new sources
of $C\!P$ violation. The study is based on a data sample of proton-proton
collisions recorded with the LHCb experiment, corresponding to an integrated
luminosity of $3$ $\mathrm{fb}^{-1}$. The $\Lambda^0_b \to p K^- \mu^+ \mu^-$
decay is observed for the first time, and two observables that are sensitive to
different manifestations of $C\!P$ violation are measured,
$\Delta\mathcal{A}_{C\!P} \equiv \mathcal{A}_{C\!P}(\Lambda^0_b \to p K^- \mu^+
\mu^-)-\mathcal{A}_{C\!P}(\Lambda^0_b\to pK^- J/\psi)$ and
$a_{C\!P}^{\widehat{T}-odd}$, where the latter is based on asymmetries in the
angle between the $\mu^+\mu^-$ and $p K^-$ decay planes. These are measured to
be $\Delta\mathcal{A}_{C\!P} = (-3.5 \pm 5.0(stat) \pm 0.2(syst))\times
10^{-2}$, $a_{C\!P}^{\widehat{T}-odd} = (1.2 \pm 5.0(stat) \pm 0.7(syst))\times
10^{-2}$, and no evidence for $C\!P$ violation is found.

Measurements of $CP$ observables in $B^{\pm} \rightarrow D K^{*\pm}$ decays
are presented, where $D$ denotes a superposition of $D^0$ and $\overline{D^0}$
meson states. Decays of the $D$ meson to $K^{-}\pi^{+}$, $K^{-}K^{+}$,
$\pi^{-}\pi^{+}$, $K^{-}\pi^{+}\pi^{-}\pi^{+}$ and
$\pi^{-}\pi^{+}\pi^{-}\pi^{+}$ are used and the $K^{*\pm}$ meson is
reconstructed in the $K^{0}_{\mathrm{S}}\pi^{\pm}$ final state. This analysis
uses a data sample of $pp$ collisions collected with the LHCb experiment,
corresponding to integrated luminosities of 1 $\mathrm{fb}^{-1}$, 2
$\mathrm{fb}^{-1}$ and 1.8 $\mathrm{fb}^{-1}$ at centre-of-mass energies
$\sqrt{s} = $ 7 TeV, 8 TeV and 13 TeV, respectively. The sensitivity of the
results to the CKM angle $\gamma$ is discussed.

A flavour-tagged decay-time-dependent amplitude analysis of
$B_s^0\to(K^+\pi^-)(K^-\pi^+)$ decays is presented in the $K^{\pm}\pi^{\mp}$
mass range from 750 to 1600 MeV$/c^2$. The analysis uses $pp$ collision data
collected with the LHCb detector at centre-of-mass energies of $7$ and $8$ TeV,
corresponding to an integrated luminosity of $3.0$ fb$^{-1}$. Several
quasi-two-body decay modes are considered, corresponding to $K^{\pm}\pi^{\mp}$
combinations with spin 0, 1 and 2, which are dominated by the $K_0^*(800)^0$
and $K_0^*(1430)^0$, the $K^*(892)^0$ and the $K_2^*(1430)^0$ resonances,
respectively. The longitudinal polarisation fraction for the $B_s^0\to
K^*(892)^0\overline{K}^*(892)^0$ decay is measured as $f_L=0.208 \pm 0.032 \pm
0.046$, where the first uncertainty is statistical and the second is
systematic. The first measurement of the mixing-induced $CP$-violating phase,
$\phi_s^{d\overline{d}}$, in $b\to d\overline{d}s$ transitions is performed,
yielding a value of $\phi_s^{d\overline{d}}=-0.10$ $\pm$ $0.13$ (stat) $\pm$
$0.14$ (syst) rad.

The CUORE experiment, a ton-scale cryogenic bolometer array, recently began
operation at the Laboratori Nazionali del Gran Sasso in Italy. The array
represents a significant advancement in this technology, and in this work we
apply it for the first time to a high-sensitivity search for a
lepton-number--violating process: $^{130}$Te neutrinoless double-beta decay.
Examining a total TeO$_2$ exposure of 86.3 kg$\cdot$yr, characterized by an
effective energy resolution of (7.7 $\pm$ 0.5) keV FWHM and a background in the
region of interest of (0.014 $\pm$ 0.002) counts/(keV$\cdot$kg$\cdot$yr), we
find no evidence for neutrinoless double-beta decay. The median statistical
sensitivity of this search is $7.0\times10^{24}$ yr. Including systematic
uncertainties, we place a lower limit on the decay half-life of
$T^{0\nu}_{1/2}$($^{130}$Te) > $1.3\times 10^{25}$ yr (90% C.L.). Combining
this result with those of two earlier experiments, Cuoricino and CUORE-0, we
find $T^{0\nu}_{1/2}$($^{130}$Te) > $1.5\times 10^{25}$ yr (90% C.L.), which is
the most stringent limit to date on this decay. Interpreting this result as a
limit on the effective Majorana neutrino mass, we find $m_{\beta\beta}<(110 -
520)$ meV, where the range reflects the nuclear matrix element estimates
employed.

A search for the lepton-flavour violating decays $B^0_s \rightarrow e^\pm
\mu^\mp$ and $B^0 \rightarrow e^\pm \mu^\mp$ is performed based on a sample of
proton-proton collision data corresponding to an integrated luminosity of 3
fb$^{-1}$, collected with the LHCb experiment at centre-of-mass energies of 7
and 8 TeV. The observed yields are consistent with the background-only
hypothesis. Upper limits on the branching fractions are determined to be
$\mathcal{B}(B^0_s \rightarrow e^\pm \mu^\mp) < 5.4\,(6.3) \times 10^{-9}$ and
$\mathcal{B}(B^0 \rightarrow e^\pm \mu^\mp) < 1.0\,(1.3) \times 10^{-9}$ at
$90\%\,(95\%)$ confidence level, which are the strongest limits on these decays
to date.

A measurement is reported of the ratio of branching fractions
$\mathcal{R}(J/\psi)=\mathcal{B}(B_c^+\,\to\,J/\psi\tau^+\nu_\tau)/\mathcal{B}(B_c^+\,\to\,J/\psi
\mu^+\nu_\mu)$, where the $\tau^+$ lepton is identified in the decay mode
$\tau^+\,\to\,\mu^+\nu_\mu\overline{\nu}_\tau$. This analysis uses a sample of
proton-proton collision data corresponding to 3.0$\mathrm{\,fb}^{-1}$ of
integrated luminosity recorded with the LHCb experiment at center-of-mass
energies $7\,\mathrm{TeV}$ and $8\,\mathrm{TeV}$. A signal is found for the
decay $B_c^+\,\to\,J/\psi \tau^+\nu_\tau$ at a significance of 3 standard
deviations, corrected for systematic uncertainty, and the ratio of the
branching fractions is measured to be $\mathcal{R}(J/\psi) = 0.71 \pm 0.17
\mathrm{\,(stat)} \pm 0.18\mathrm{\,(syst)}$. This result lies within 2
standard deviations above the range of existing predictions in the Standard
Model.

The cross-section for inelastic proton-proton collisions at a centre-of-mass
energy of 13\,TeV is measured with the LHCb detector. The fiducial
cross-section for inelastic interactions producing at least one prompt
long-lived charged particle with momentum $p>2$\,GeV/$c$ in the pseudorapidity
range $2<\eta<5$ is determined to be $\sigma_{\rm acc}= 62.2 \pm 0.2 \pm
2.5$\,mb. The first uncertainty is the intrinsic systematic uncertainty of the
measurement, the second is due to the uncertainty on the integrated luminosity.
The statistical uncertainty is negligible. Extrapolation to full phase space
yields the total inelastic proton-proton cross-section $\sigma_{\rm inel}= 75.4
\pm 3.0 \pm 4.5$\,mb, where the first uncertainty is experimental and the
second due to the extrapolation. An updated value of the inelastic
cross-section at a centre-of-mass energy of 7\,TeV is also reported.

The $CP$ asymmetry in $B^-\to D_s^-D^0$ and $B^-\to D^-D^0$ decays is
measured using LHCb data corresponding to an integrated luminosity of 3.0
fb$^{-1}$, collected in $pp$ collisions at centre-of-mass energies of 7 and 8
TeV. The results are $A^{CP}(B^-\to D_s^-D^0)=(-0.4\pm 0.5\pm 0.5)\%$ and
$A^{CP}(B^-\to D^-D^0)=( 2.3\pm 2.7\pm 0.4)\%$, where the first uncertainties
are statistical and the second systematic. This is the first measurement of
$A^{CP}(B^-\to D_s^-D^0)$ and the most precise determination of $A^{CP}(B^-\to
D^-D^0)$. Neither result shows evidence of $CP$ violation.